Parsimonious estimation of sex-specific map distances by stepwise maximum likelihood regression

In human genetic maps, differences between female (xf) and male (xm) map distances may be characterized by the ratio, R = xf/xm, or the relative difference, Q = (xf - xm)/(xf + xm) = (R - 1)/(R + 1). For a map of genetic markers spread along a chromosome, Q(d) may be viewed as a graph of Q versus the midpoints, d, of the map intervals. To estimate male and female map distances for each interval, a novel method is proposed to evaluate the most parsimonious trend of Q(d) along the chromosome, where Q(d) is expressed as a polynomial in d. Stepwise maximum likelihood polynomial regression of Q is described. The procedure has been implemented in a FORTRAN program package, TREND, and is applied to data on chromosome 18.